Abstract:

We consider repeated two-person zero-sum games where the number of repetitions theta is unknown. The information about the uncertain duration is identical to both players and can change during the play of the game. This is described by an uncertain duration process Theta. To each repeated game Gamma and uncertain duration process Theta is associated the Theta repeated game Gamma_Theta with value V_Theta. We establish a recursive formula for the value V_Theta. We study asymptotic properties of the value v_Theta=V_Theta/E(theta) as the expected duration E(theta) goes to infinity. We extend and unify several asymptotic results on the existence of lim v_n and lim v_lambda and their equality to lim v_Theta. This analysis applies in particular to stochastic games and repeated games of incomplete information.

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